Results 31 to 40 of about 12,988 (199)

Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model

Mathematical Biosciences and Engineering, 2017
This paper studies the global existence and uniqueness of classicalsolutions for a generalized quasilinear parabolic equation withappropriate initial and mixed boundary conditions.
Zijuan Wen, Meng Fan, Asim M. Asiri, Ebraheem O. Alzahrani, Mohamed M. El-Dessoky, Yang Kuang   +5 more
doaj   +1 more source

Multivalued solutions of multidimensional linear equations of heat conduction and rivertons

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2021
Background. The article considers the problem of calculating multivalued solutions of multidimensional linear parabolic equations. Solutions for this type of equations of heat conductivity in dimension d > 2 were not previously known and represent an ...
V.M. Zhuravlev, V.M. Morozov
doaj   +1 more source

Global Sobolev Solutions of Quasilinear Parabolic Equations

Differential and Integral Equations, 1998
Global existence, uniqueness and a priori estimates of solutions to the initial and homogeneous Dirichlet boundary value problem for the equation \[ u_t - \sum _{i,j=1}^{n} a_{i,j}(\nabla u) \partial _i \partial _j u = f(x,t)\quad\text{on} \Omega \times (0,T) \] is proved in Sobolev spaces \(X_{s+2}(T)\) for sufficiently large \(s.\) Here \[ X_m(T) = \{
McLeod, Kevin, Milani, Albert
openaire   +3 more sources

On the principle of linearized stability for quasilinear evolution equations in time‐weighted spaces

Mathematische Nachrichten, Volume 298, Issue 12, Page 3939-3959, December 2025.
Abstract Quasilinear (and semilinear) parabolic problems of the form v′=A(v)v+f(v)$v^{\prime }=A(v)v+f(v)$ with strict inclusion dom(f)⊊dom(A)$\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function v↦f(v)$v\mapsto f(v)$ and the quasilinear part v↦A(v)$v\mapsto A(v)$ are considered in the framework of time‐weighted function spaces ...
Bogdan‐Vasile Matioc, Lina Sophie Schmitz, Christoph Walker   +2 more
wiley   +1 more source

Localized peaking regimes for quasilinear parabolic equations

, 2018
This paper deals with the asymptotic behavior as $t\rightarrow T1, \end{equation*} with prescribed global energy function \begin{equation*} E(t):=\int_{\Omega}|u(t,x)|^{p+1}dx+ \int_0^t\int_{\Omega}|\nabla_xu(\tau,x)|^{p+1}dxd\tau \rightarrow\infty ...
Shishkov, Andrey E., Yevgenieva, Yevgeniia A.   +1 more
core   +1 more source

Quasilinear Degenerate Evolution Systems Modelling Biofilm Growth: Well‐Posedness and Qualitative Properties

Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 14890-14908, 15 November 2025.
ABSTRACT We analyze nonlinear degenerate coupled partial differential equation (PDE)‐PDE and PDE‐ordinary differential equation (ODE) systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion.
K. Mitra, S. Sonner
wiley   +1 more source

On the solvability of some parabolic equations involving nonlinear boundary conditions with L^{1} data [PDF]

Opuscula Mathematica
We analyze the existence of solutions for a class of quasilinear parabolic equations with critical growth nonlinearities, nonlinear boundary conditions, and \(L^1\) data.
Laila Taourirte, Abderrahim Charkaoui, Nour Eddine Alaa   +2 more
doaj   +1 more source

Muskat–Leverett Two‐Phase Flow in Thin Cylindric Porous Media: Asymptotic Approach

Studies in Applied Mathematics, Volume 155, Issue 5, November 2025.
ABSTRACT A reduced‐dimensional asymptotic modeling approach is presented for the analysis of two‐phase flow in a thin cylinder with an aperture of order O(ε)$\mathcal {O}(\varepsilon)$, where ε$\varepsilon$ is a small positive parameter. We consider a nonlinear Muskat–Leverett two‐phase flow model expressed in terms of a fractional flow formulation and
Taras Mel'nyk, Christian Rohde
wiley   +1 more source

Multidimensional Stability of Planar Traveling Waves for Stochastically Perturbed Reaction–Diffusion Systems

Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.
ABSTRACT We consider reaction–diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, colored in space, and invariant under translations. Inspired by previous works on the real line, we establish the multidimensional stability of planar waves on a cylindrical domain on timescales ...
M. van den Bosch, H. J. Hupkes
wiley   +1 more source

Regularity for a class of quasilinear degenerate parabolic equations in the Heisenberg group

Mathematics in Engineering, 2021
We extend to the parabolic setting some of the ideas originated with Xiao Zhong's proof in [31] of the Hölder regularity of $p-$harmonic functions in the Heisenberg group $\mathbb{H}^n$. Given a number $p\ge 2$, in this paper we establish the $C^{\infty}$
Luca Capogna, Giovanna Citti, Nicola Garofalo   +2 more
doaj   +1 more source